This study, summarized in two parts, is directed at the investigation of the non-linear performance of Nomex, Kevlar and polypropylene fibres, when undergoing stress relaxation tests. The description of the strain-dependent performance is based on a two-component model, which comprises an elastic and a viscous contribution. A shape-invariant relaxation function is introduced that is based on the cumulative log-normal distribution. This first part is directed at the description of the experimental procedures and of the approach to the analysis of the stress relaxation data.